Question: Is ${564076}$ divisible by $4$ ?
A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{5640} {76} = \gray{5640} \gray{00} + {76} $ Because $564000$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${76}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $76$ , divisible by $4$ Yes, ${76 \div 4 = 19}$, so $564076$ must also be divisible by $4$.